Tables for
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 2.1, p. 146


Th. Hahna and M. I. Aroyoc

Table| top | pdf |
Graphical symbols of symmetry planes normal to the plane of projection (three dimensions) and symmetry lines in the plane of the figure (two dimensions)

DescriptionGraphical symbolGlide vector(s) of the defining operation(s) of the glide plane (in units of the shortest lattice translation vectors parallel and normal to the projection plane)Symmetry element represented by the graphical symbol
[\left.\openup3pt\matrix{\hbox{Reflection plane, mirror plane}\hfill\cr \hbox{Reflection line, mirror line (two dimensions)}\cr}\right\}] [Scheme scheme14] None m
[\left.\openup3pt\matrix{\hbox{`Axial' glide plane}\hfill\cr\hbox{Glide line (two dimensions)}\cr}\right\}] [Scheme scheme15] [\!\openup2pt\matrix{{1 \over 2} \hbox{parallel to line in projection plane}\cr {1 \over 2} \hbox{parallel to line in figure plane}\hfill\cr}] [\!\matrix{a,\ b \hbox{ or } c\cr g\hfill\cr}]
`Axial' glide plane [Scheme scheme16] [{1 \over 2}] normal to projection plane a, b or c
`Double' glide plane [Scheme scheme17] [\!\openup2pt\matrix{Two\hbox{ glide vectors:}\hfill\cr{1 \over 2}\hbox{ parallel to line in, and}\hfill\cr{1 \over 2} \hbox{ normal to projection plane}\hfill}] e
`Diagonal' glide plane [Scheme scheme18] [\!\openup2pt\matrix{One\hbox{ glide vector with }two\hbox{ components:}\hfill\cr{1 \over 2}\hbox{ parallel to line in, and}\hfill\cr{1 \over 2}\hbox{ normal to projection plane}\hfill}] n
`Diamond' glide plane (pair of planes) [Scheme scheme19] [{1 \over 4}] parallel to line in projection plane, combined with [{1 \over 4}] normal to projection plane (arrow indicates direction parallel to the projection plane for which the normal component is positive) d
The graphical symbols of the `e'-glide planes are applied to the diagrams of seven orthorhombic A-, C- and F-centred space groups, five tetragonal I-centred space groups, and five cubic F- and I-centred space groups.
Glide planes d occur only in orthorhombic F space groups, in tetragonal I space groups, and in cubic I and F space groups. They always occur in pairs with alternating glide vectors, for instance [{1 \over 4}({\bf a} + {\bf b})] and [{1 \over 4}({\bf a} - {\bf b})]. The second power of a glide reflection d is a centring vector.